Averaged coordination numbers of planar aperiodic tilings
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چکیده
We consider averaged shelling and coordination numbers of aperiodic tilings. Shelling numbers count the vertices on radial shells around a vertex. Coordination numbers, in turn, count the vertices on coordination shells of a vertex, defined via the graph distance given by the tiling. For the Ammann-Beenker tiling, we find that coordination shells consist of complete shelling orbits, which enables us to calculate averaged coordination numbers for rather large distances explicitly. The relation to topological invariants of tilings is briefly discussed.
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The Open University ’ s repository of research publications and other research outputs Averaged coordination numbers of planar aperiodic tilings
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The Open University ’ s repository of research publications and other research outputs Averaged coordination numbers of planar aperiodic
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